Thermodynamics PYQs Set 13 (PDF)

Set 13 of 17 · Questions 361-390 of 484

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Mere Teacher · Previous Year Questions JEE Main Physics · Thermodynamics · Set 13 (Q361-390)
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361. $Using the given P - V diagram, the work done by an ideal gas along the path ABCD is:$ (1) $3 P_{0} V_{0}$ (2) $- 4 P_{0} V_{0}$ (3) $- 3 P_{0} V_{0}$ (4) $4 P_{0} V_{0}$ 362. $thermodynamic process is shown below on a P - V diagram for one mole of an ideal gas. If V_{2} = 2 V_{1} then theratio of temperature T_{2} / T_{1} is:$ (1) $\frac{1}{2}$ (2) $\frac{1}{2}$ (3) $2$ (4) $2$ 363. $A thermodynamic system is taken from an original state D to an intermediate state E by the linear process shown in the figure. Its volume is then reduced to the original volume from E to F by an isobaric process. The total work done by the gas from D to E to F will be$ (1) $-450J$ (2) $450J$ (3) $900J$ (4) $350J$ 364. $A heat engine employing a Carnot cycle with an efficiency of η = 10% is used as a refrigerating machine, the thermal reservoirs being the same. The refrigerating efficiency \in is$ (1) $12$ (2) $8$ (3) $\frac{1}{10}$ (4) $9$ 365. $The given figure represents two isobaric processes for the same mass of an ideal gas, then$ (1) $P_{2} \geq P_{1}$ (2) $P_{2} > P_{1}$ (3) $P_{1} = P_{2}$ (4) $P_{1} > P_{2}$ 366. $A Carnot engine working between 300 K and 600K has a work out put of 800 J per cycle. The amount of heat energy supplied to the engine from the source in each cycle is -$ (1) $800 J$ (2) $1600 J$ (3) $3500 J$ (4) $6400 J$ 367. $A sample of an ideal gas is taken through the cyclic process ABCA as shown in figure. It absorbs, 40 J of heat during the part AB, no heat during BC and rejects 60J of heat during CA. A work 50J is done on the gas during the part BC. The internal energy of the gas at A is 1560J. The work done by the gas during the part CA is:$ (1) $20J$ (2) $30J$ (3) $-30J$ (4) $-60 J$ 368. $For three low density gases A, B, C pressure versus temperature graphs are plotted while keeping them at constant volume, as shown in the figure. The temperature corresponding to the point 'K' is:$ (1) $-273°C$ (2) $-100°C$ (3) $-373°C$ (4) $-40°C$ 369. $Two Carnot engines A and B operate in series such that engine A absorbs heat at T_{1} and rejects heat to a sink at temperature T. Engine B absorbs half of the heat rejected by Engine and rejects heat to the sink at T_{3} . When work done in both the cases is equal, to value of T is:$ (1) $\frac{2}{3} T_{1} + \frac{3}{2} T_{3}$ (2) $\frac{1}{3} T_{1} + \frac{2}{3} T_{3}$ (3) $\frac{3}{2} T_{1} + \frac{1}{3} T_{3}$ (4) $\frac{2}{3} T_{1} + \frac{1}{3} T_{3}$ 370. $An ideal gas at pressure P_{0} - undergoes an isothermal expansion until its volume is 8.0 times its initial volume. The gas is slowly and adiabatically compressed back to its original volume. If the adiabatic constant of the gas is γ = 4/3, then the ratio of the average kinetic energy per molecule in this final state to that in the initial state is$ (1) $1.44$ (2) $1.68$ (3) $2.0$ (4) $1.2$ 371. $The p - V diagram for an ideal gas in a piston cylinder assembly undergoing a thermodynamic process is shown in the figure. The process is [NEET 2020]$ (1) $adiabatic$ (2) $isochoric$ (3) $isobaric$ (4) $isothermal$ 372. $An ideal gas undergoes four different processes from the same initial state as shown in the figure below. Those processes are adiabatic, isothermal, isobaric and isochoric. The curve which represents the adiabatic process among 1, 2, 3 and 4 is [NEET 2022]$ (1) $2$ (2) $3$ (3) $4$ (4) $1$ 373. $Consider a gas of triatomic molecules. The molecules are assumed to be triangular and made of massless rigid rods whose vertices are occupied by atoms. The internal energy of a mole of the gas at temperature T is$ (1) $3 RT$ (2) $\frac{9}{2} RT$ (3) $\frac{3}{2} RT$ (4) $\frac{5}{2} RT$ 374. $For a given mass of a gas at constant temperature, the volume and the pressure are V and P respectively. Then the slope of the graph drawn between log_{e} V on X -axis and log_{e} P on Y-axis is$ (1) $1$ (2) $-1$ (3) $Zero$ (4) $Infinity$ 375. $A thermodynamic system is taken through the cycle ABCD as shown in figure. Heat rejected$ (1) $2 PV$ (2) $4 PV$ (3) $12 PV$ (4) $PV$ 376. $In a steady state, the temperature at the end A and end B of a 20 cm long rod AB are 100^{\circ} C and 0^{\circ} C . The temperature of a point 9 cm from A is$ (1) $55^{\circ} C$ (2) $45^{\circ} C$ (3) $65^{\circ} C$ (4) $50^{\circ} C$ 377. $The heat absorbed by a system in going through the given cyclic process is :$ (1) $19.6 J$ (2) $61.6 J$ (3) $616 J$ (4) $431.2 J$ 378. $An ideal gas exists in a state with pressure P_{0}, volume V_{0} . It is isothermally expanded to 4 times of its initial volume (V_{0}), then isobarically compressed to its original volume. Finally the system is heated isochorically to bring it to its initial state. The amount of heat exchanged in this process is$ (1) $P_{0} V_{0} (ln 2 - 0.75)$ (2) $P_{0} V_{0} (2 ln 2 - 0.75)$ (3) $P_{0} V_{0} (2 ln 2 - 0.25)$ (4) $P_{0} V_{0} (ln 2 - 0.25)$ 379. $Two different adiabatic paths for the same gas intersect two isothermal curves as shown in P-V diagram. The relation between the ratio \frac{V _{a}}{V _{d}} and the ratio \frac{V _{b}}{V _{c}} is:$ (1) $\frac{V _{a}}{V _{d}} \neq = \frac{V _{b}}{V _{c}}$ (2) $\frac{V _{a}}{V _{d}} = \frac{V _{b}}{V _{c}}$ (3) $\frac{V _{a}}{V _{d}} = (\frac{V _{b}}{V _{c}})^{- 1}$ (4) $\frac{V _{a}}{V _{d}} = (\frac{V _{b}}{V _{c}})^{2}$ 380. $The cycle is shown in figure is followed by an engine made of one mole of perfect gas in a cylinder with a piston. The processes A to B and C to D are isochoric whereas process B to C and D to A are adiabatic, the work done by the engine in one cycle is (V_{A} = V_{B} = V, V_{C} = V_{D} = 2V and g = 5/3)$ (1) $[1 - 4^{3/2}] (P_{B} - P_{A}) V$ (2) $\frac{3}{2} [1 - 3^{2/3}] (P_{B} - P_{A}) V$ (3) $\frac{3}{2} [1 - 2^{-2/3}] (P_{B} - P_{A}) V$ (4) $\frac{5}{2} [1 - 2^{-2/3}] (P_{B} - P_{A}) V$ 381. $Three moles of an ideal monoatomic gas performs a cycle ABCDA as shown in the figure. The temperatures of the gas at the states A, B, C and D are 400 K, 800 K, 2400 K and 1200 K, respectively. The work done by the gas during this cycle is (R is universal gas constant)$ (1) $1200 R$ (2) $3600 R$ (3) $2400 R$ (4) $2000 R$ 382. $There are two vessels filled with an ideal gas where volume of one is double the volume of other. The large vessel contains the gas at 8 kPa at 1000 K while the smaller vessel contains the gas at 7 kPa at 500 K. If the vessels are connected to each other by a thin tube allowing the gas to flow and the temperature of both vessels is maintained at 600 K, at steady state the pressure in the vessels will be (in kPa).$ (1) $24$ (2) $4.4$ (3) $18$ (4) $6$ 383. $An aluminum rod of length 1 m and a steel rod of length 2 m both having same cross-sectional area, are soldered together end-to-end. The thermal conductivity of aluminum rod and steel rod is 200 Js^{- 1} m^{- 1} K^{- 1} and 50 Js^{- 1} m^{- 1} K^{- 1} respectively. The temperatures of the free ends are maintained at 300 K and 500 K . What is the temperature of the junction?$ (1) $322 K$ (2) $350 K$ (3) $367 K$ (4) $400 K$ 384. $In the cyclic process given in the P - V diagram, the work done is$ (1) $π (\frac{P _{2} - P _{1}}{2})^{2}$ (2) $π (\frac{V _{2} - V _{1}}{2})^{2}$ (3) $π (P_{2} V_{2} - P_{1} V_{1})$ (4) $\frac{π}{4} (P_{2} - P_{1}) (V_{2} - V_{1})$ 385. $A circular copper ring at 30^{\circ} C has a hole with an area of 9.98 cm^{2} . It is made to slip onto a steel rod of cross-sectional area of 10 cm^{2}, by raising the temperature of both ring and rod simultaneously by an amount Δ T . If the coefficient of linear expansion of copper and steel are 17 \times 10^{- 6} /° C and 11 \times 10^{- 6} /° C, then minimum value of Δ T should be$ (1) $167.6^{\circ} C$ (2) $133.3^{\circ} C$ (3) $83.3^{\circ} C$ (4) $249.9^{\circ} C$ 386. $One mole of an ideal diatomic gas undergoes a transition from A to B along a path AB as shown in the figure. The change in internal energy of the gas during the transition is$ (1) $20 kJ$ (2) $-20 kJ$ (3) $20 J$ (4) $-12 kJ$ 387. $The pressure of a gas changes linearly with volume from A to B as shown in figure. If no heat is supplied to or extracted from the gas then change in the internal energy of the gas will be$ (1) $6J$ (2) $Zero$ (3) $-4.5J$ (4) $4.5J$ 388. $A cycle followed by an engine (made of one mole of an ideal gas in a cylinder with a piston) is shown in figure. The heat exchanged by the engine with the surroundings at constant volume is (Take C_{V} = \frac{3}{2} R)$ (1) $(P_{B} - P_{A}) V_{A}$ (2) $\frac{1}{2} (P_{B} - P_{A}) V_{A}$ (3) $\frac{3}{2} (P_{B} - P_{A}) V_{A}$ (4) $\frac{5}{2} (P_{B} - P_{A}) V_{A}$ 389. $A thermodynamic system is taken through the cyclic process ABC as shown in the figure. The total work done by the system during the cycle ABC is____J.$ 390. $An ideal gas has undergone through the cyclic process as shown in the figure. Work done by the gas in the entire cycle is _______\times 10^{- 1} J . (Take π = 3.14)$